Geodesic
Ergodicity and conservativity of products of infinite transformations and their inverses
Julien Clancy 1   ; Rina Friedberg 2   ; Indraneel Kasmalkar 3   ; Isaac Loh 4   ; Tudor Pădurariu 5   ; Cesar E. Silva 6   ; Sahana Vasudevan 7
1 Yale University New Haven, CT 06520, U.S.A.
2 University of Chicago Chicago, IL 60637, U.S.A.
3 University of California, Berkeley Berkeley, CA 94720, U.S.A.
4 Williams College Williamstown, MA 01267, U.S.A.
5 University of California Los Angeles, CA 90095-1555, U.S.A.
6 Department of Mathematics Williams College Williamstown, MA 01267, U.S.A.
7 Harvard University Cambridge, MA 02138, U.S.A.
Colloquium Mathematicum, Tome 143 (2016) no. 2, pp. 271-291 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ is ergodic, but the product $T\times T^{-1}$ is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.
DOI : 10.4064/cm6482-10-2015
Keywords: construct class rank one infinite measure preserving transformations each transformation class cartesian product times ergodic product times prove product rank one transformation its inverse conservative while there infinite measure preserving conservative ergodic markov shifts whose product their inverse conservative

Julien Clancy  1   ; Rina Friedberg  2   ; Indraneel Kasmalkar  3   ; Isaac Loh  4   ; Tudor Pădurariu  5   ; Cesar E. Silva  6   ; Sahana Vasudevan  7

1 Yale University New Haven, CT 06520, U.S.A.
2 University of Chicago Chicago, IL 60637, U.S.A.
3 University of California, Berkeley Berkeley, CA 94720, U.S.A.
4 Williams College Williamstown, MA 01267, U.S.A.
5 University of California Los Angeles, CA 90095-1555, U.S.A.
6 Department of Mathematics Williams College Williamstown, MA 01267, U.S.A.
7 Harvard University Cambridge, MA 02138, U.S.A. 
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     author = {Julien Clancy and Rina Friedberg and Indraneel Kasmalkar and Isaac Loh and Tudor P\u{a}durariu and Cesar E. Silva and Sahana Vasudevan},
     title = {Ergodicity and conservativity of products of infinite transformations and their inverses},
     journal = {Colloquium Mathematicum},
     pages = {271--291},
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     number = {2},
     doi = {10.4064/cm6482-10-2015},
     language = {en},
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Julien Clancy; Rina Friedberg; Indraneel Kasmalkar; Isaac Loh; Tudor Pădurariu; Cesar E. Silva; Sahana Vasudevan. Ergodicity and conservativity of products of infinite transformations and their inverses. Colloquium Mathematicum, Tome 143 (2016) no. 2, pp. 271-291. doi: 10.4064/cm6482-10-2015

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